Finance and Stochastics

, Volume 20, Issue 1, pp 219–265 | Cite as

Short-time expansions for close-to-the-money options under a Lévy jump model with stochastic volatility

Article

Abstract

In Figueroa-López et al. (Math. Finance, 2013), a second order approximation for at-the-money option prices is derived for a large class of exponential Lévy models, with or without a Brownian component. The purpose of the present article is twofold. First, we relax the regularity conditions imposed on the Lévy density to the weakest possible conditions for such an expansion to be well defined. Second, we show that the formulas extend both to the case of “close-to-the-money” strikes and to the case where the continuous Brownian component is replaced by an independent stochastic volatility process with leverage.

Keywords

Exponential Lévy models Stochastic volatility models Short-time asymptotics ATM option pricing Implied volatility 

Mathematics Subject Classification (2010)

60G51 60F99 91G20 

JEL Classification

C6 

Notes

Acknowledgements

The authors gratefully acknowledge the constructive and helpful comments provided by two anonymous referees, which significantly contributed to improve the quality of the manuscript.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsWashington University in St. LouisSt. LouisUSA
  2. 2.Department of StatisticsPurdue UniversityWest LafayetteUSA

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